A Classical Invitation to Algebraic Numbers and Class Fields

Name: A Classical Invitation to Algebraic Numbers and Class Fields
Author: Harvey Cohn

Mitwirkende
Unterstützt von	O. Taussky
Autor / Autorin	Harvey Cohn

I. Preliminaries.
1. Introductory Remarks on Quadratic Forms.
2. Algebraic Background.
3. Quadratic Euclidean Rings.
4. Congruence Classes.
5. Polynomial Rings.
6. Dedekind Domains.
7. Extensions of Dedekind Domains.
8. Rational and Elliptic Functions.
II. Ideal Structure in Number Fields.
9. Basis and Discriminant.
10. Prime Factorization.
11. Units.
12. Geometry of Numbers.
13. Finite Determination of Class Number.
III. Introduction to Class Field Theory.
14. Quadratic Forms, Rings and Genera.
15. Ray Class Structure and Fields, Hilbert Class Fields.
16. Hilbert Sequences.
17 Discriminant and Conductor.
18. The Artin Isomorphism.
19. The Zeta-Function.
Appendices (by Olga Taussky).
Lectures on Class Field Theory by E. Artin (Göttingen 1932) Notes by O. Taussky.
into Connections Between Algebraic Number Theory and Integral Matrices (Appendix by Olga Taussky).
Subject Matter Index.